WASHINGTON (CNN) -- A day after strengthening the Republican Party's majority in the House, Speaker Dennis Hastert called on Democrats to assist GOP efforts to fight the war on terror, create jobs and expand health insurance to more Americans.

"I pledge to work with those Democrats who want to work with me to get good things done for the American people," Hastert said Wednesday.

But House Democratic leader Nancy Pelosi of California, stung by her party's losses on Election Day, seemed unlikely to accept the offer.

"The Republicans did not have an election about jobs, health care, education, environment, national security. They had an election about wedge issues in our country, and you know what they are," she said.

"They exploited the loveliness of the American people, the devoutness of people of faith for a political end."

"She lost seats," he said. "This is a demoralizing loss for House Democrats and is personally damaging to leader Pelosi."

For the 110th Congress, confident House Republicans claimed a mandate for their agenda, which includes tax cuts, tort reform and an energy bill that would allow oil drilling in Alaska's Arctic National Wildlife Refuge.

"We have a president that has won handily, and everybody thought he was in trouble. And we have a Congress that has increased [Republican] membership in both the House and the Senate," Reynolds said. "I'm ecstatic."

Republicans retained control of the House and added at least four seats to their number, joining GOP gains in the Senate to solidify the party's congressional control. In the Senate, Republicans added four seats to increase their majority to 55.

Two of the House's 435 seats remain undecided, both in Louisiana, where the final winner will be determined in a December runoff.

A controversial redistricting effort in Texas paid dividends for Republicans, who knocked off four Democratic incumbents there, including Rep. Martin Frost, a 20-year veteran and former Democratic leader. Another Democrat, Rep. Barron Hill of Indiana, also was ousted.

Only two GOP incumbents lost their seats Tuesday night: Rep. Phil Crane of Illinois, who has served in the House for 36 years, and Georgia freshman Max Burns, who had the difficult task of defending a majority Democratic district.